I store mine upside down...I suppose it really doesn't matter considering how quickly we use them and the fact that they are in a cupboard...but it drains better if there is any left over liquid from washing???

I store them right side up. They don't sit very long so I'm not worried about the dust, but even if I was, there's probably dust on the cupboard so I'm not sure there's a difference? I mean, the dust is going to slide around on the rim of the glass if it's upside down.